The only times I've cried/shown any real emotion (except laughter) during any anime, was in Naruto Shippuden, where:

-He meets his father when he turns into 9 tails against Pain.
-He meets his mother Kushina and suddenly just hugs her. (while fighting the 9 tails)
-When he hugs his inner evil self while training to take control of 9 tails.
-When Konan dies D':

It has be the Black Rock Shooter anime, by the time i connected all the dots and realized exactly what was going on, it hit me pretty hard at the end. I was sobbing and crying all night. I've gotten into a pretty bad mess with a friend a couple of summers ago, we left on a very bad note. The anime motivated me to contact her, and when I did and we made up and stuff, she found it hilarious that an anime was what pushed me to talk to her again. We were mad at e/o for the stupidest reasons until I saw how stupid it was to ruin the friendship we had for so long. So yea... BRS, if you haven't seen it, you should totally take a look at it.